Infinite Board

   

I admit I haven't read the novel "Walking on Glass" by Iain Banks, but the Literature page suggests a Go variant on an infinite goban.

Normal Go with an infinite board is rather hard to win as a new group can be started just by plonking another stone somewhere (possibly infinitely) far from the existing stones, then making it as big as you like. There isn't much point in fighting when you can get points elsewhere and ko's wandering off forever aren't very exciting to play.

My interest is in ways that the rules can be generalised into something that is playable in finite time. To do this, the rules will have to generate some reason why no further play is allowed.

An infinite board could be infinite in both dimensions, semi-infinite (one edge), quarter-infinite (two perpendicular edges), strip-infinite (two parallel edges), semi-strip-infinite (three edges), or presumably lots of other semi-bounded areas.


My first thought is to generalise the super-ko rule, such that the infinite goban is split into 19x19 areas which cannot be repeated anywhere else (but allowing an empty 19x19 board of course). As there are only finitely many legal go positions, eventually a position will arise where there are no legal moves for either player, so the game ends. Count territory in the fashion of Tromp-Taylor rules. The unused infinite area of the board will 'see' both colours and so be dame. Counting will take a while, but there will be a winner.


Another approach is to play with a finite number of moves or an absolute time limit (pass moves costing no time). In the given time, make the most moves you can so that some territory 'sees' only your colour. At first sight, both players will play far away from each other and wall off the biggest area possible with the number of stones in the time. As this will presumably be a draw (komi must surely be zero for an infinite board), perhaps an attack on or invasion inside the other player's territory is a better bet.


Anyone else got some bright ideas? ( I'm not volunteering to play test any of them!)

Siouxdenim

mAsterdam: Would this work? The game is over as soon as one color's territory is n (say 5) points bigger than the other's.

Handicap would mean the placement of (infinitely many) stones on every m-th intersection in every direction. The smaller m, the bigger the handicap, of course.

DougRidgway: Another approach is to give a different weighting to different locations. So, e.g. area scoring, score for owning (x,y) = exp(-x^2-y^2), and there will be a finite total possible score. Play will stop eventually because the outer reaches are infinitesimally close to dame.

The real question is, do ladders work?


If the outer edges are infinitesimally close to 0 but there are infinitely many of them, tedomari will take a very long time.

SiouxDenim


This is a copy of the living page "Infinite Board" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.
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